2. Let y 3x23 a) Find the change in y, Ay when x = 5 and Ax b) Find the differential dy when x 5 and dx

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Q: Solve the given differential equation. 5ydx-5xdy + xdx=9dx

A: 5ydx-5xdy+x7dx=9dxwe know  d(yx)=xdy-ydxx2∫xndx=xn+1n+1+c

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A: Find the centroid of the region cut from the first quadrant by the circle x2+y2=81.

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A: Given: y=2x2-5 on 0≤x≤1 To find: Arc length.

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A: The family of cones given by the equation:   x^2 + y^2 - a^2*z^2 = 0

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Q: 2 Find the average height of the paraboloid z = x +y over the square 0 ≤x≤ 1,0 ≤ y ≤ 1

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Q: 3. a) Find the limit of the sequence an = (2n²+3)(n-1) n(n² + 1)

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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A: Given: y = 4x2 x = 1  y = 0 about x-axis

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A: Given:- Revenue function Rx=7600xCost function Cx=x3-2x2+5x+100

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Q: Sketch the graph that possesses the characteristics listed. f is concave down at (1,5), concave up…

A: We need to find the graph which have the following characteristics f is concave down at point (1,5)…

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Q: Find the distance from the point (4,-4,-5) to the line a(t) = (3, 1, − 4)t + (9,- 5,3)

A: Given equation of line:- a→t=3,1,-4t+9,-5,3

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Q: The gradient of f(x, y) = zy at (x, y) = (-1,1) is

A: The gradient of function f(x,y) is represented by ∇f(x,y) where:∇f(x,y)=∂f∂x,∂f∂y          Equation…

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A: given  Fs=8 s2 - 49 s + 294s  s2 + 49 and asked to find the inverse laplace transform of F( s ).

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Q: Write a rational function whose graph is shown below. -1 + 2 0 -2- T 1 1 + 2 F L 3 + 1 (4,0) 4 1 -10…

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Q: Given (y)-16-²-², use the total differential to approximate or at (4.1) towards (24,1.05). Round…

A: △x=2.4-4=-1.6△y=1.05-1=0.05

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A: We have given the equation of tangent line y=5x-6 of f(x) at point (2,4).

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A: f(x,y)=5-4x+6y-3x2y∂ ∂x(xn)=nxn-1∂ ∂x(constnat)=0

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A: Given curves: y=x4, y=1 To find: Volume of solid obtained by rotating the region bounded by the…

Q: Describe the given region in polar coordinates.

A: Please see the below picture for detailed solution.

Q: Question 17 () Let / be defined as follows: {² z Using the definition of the derivative, compute…

A: Let f be defined as follows:  fx=x2 if x<0x if x≥0 By using the definition of derivative, to…

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A: Consider the graph between two curves. To determine the set up of integral  that represents the area…

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Q: The cost of producing x bags of dog food is given by C(x) = 900+√700 + 50x²-x where 0≤x≤ 5000. Find…

A: The cost of producing x bags of dog food is given by Cx=900+700+50x2-x, where 0≤x≤5000. To find the…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x², y = 0, and x = 1,…

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